Framework

Let’s name each gear. The gear number is labelled with name and is composed of teeth:

Right angle transmission

Let’s have a look at the right angle transmission:

This is a classical right angle gear, the transmission is given by:

and

We will no longer consider this transmission in the following.

Carrier’s frame

We will now work in a new referential attached to the carrier and focus on gears , , and . The term is the angular velocity of gear expressed in the carrier’s referential.

According to the previous direction of rotation, the transmissions between gears , , and are given by:

Note that the gear is redundant with the gear . The relation between gear and is given by:

As , the relation between angular velocities is :

Global frame

Let’s now come back in the global referential. The carrier angular velocity is given by . In the carrier’s referential, the angular velocity of gear gear is equal to . The angular velocity of gear in the global referential is thus given by:

With the same reasoning, we can also express the angular velocity of gear in the global referential: